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Unformatted text preview: ChemE 178: Homework #6 Solutions 1.) Polymer blends are to be made from a poly(ethylenepropylene) (hPEP) of weight average molecular weight Mw = 175,000, Mw/Mn=1.01 and a perdeuterated poly(ethylenepropylene) (dPEP), Mw=200,000, Mw/Mn=1.01. The dPEP is the same in all respect as the hPEP except that the dPEP has all hydrogens exchanged for deuterium. The Flory parameter for the dPEP/hPEP pair is given by = (0.571/T)6.6x104 , where T is the absolute temperature (K). Compute and plot the following: _______________________________________________________________________ _ A.) The normalized free energy of mixing G mix /Mk B T versus dPB at the following temperatures: 300K, 350K, 385K and 450K. Use a spreadsheet program like Excel or a plotting program with computational capability to produce these plots. Use scales so that important details are visible. Begin with the FloryHuggins Equation: ( 29 ( 29 ln ln A B A B A B B A B G Mk T N N = + + To get N A and N B , you will need to use the number average molecular weight. dPEP: 200,000 198,020 1.01 w n M M PDI = = = hPEP: 175,000 173,267 1.01 w n M M PDI = = = Assuming that the hPEP and dPEP have similar monomeric volumes, the segment lengths are simply the degree of polymerization. Note: This is not always the case. 173,267 2,475 70 198,020 2,475 80 h PEP A d PEP B N N N N = = = = = = The polymer blend is incompressible, so 1 A B = + Given the expression for , you can use the FloryHuggins equation to plot the normalized free energy as a function of volume fraction. Gibbs Energy of Mixing1.40E041.20E041.00E048.00E056.00E054.00E052.00E05 0.00E+00 2.00E05 4.00E05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (dPB) G/MkT 300 K 350 K 385 K 450 K B.) Compute the binodal and spinodal 's as a function of temperature and use these to compute and plot the phase diagram for this system. The binodal is define as ( 29 ( 29 ( 29 1 2 1 1 ln 1 ln 1 1 2 A A mix mix A B A A A A B G G N N = = + + + The binodal is calculated using the condition that binodal point lies on the same...
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This note was uploaded on 12/09/2011 for the course CHEM ENG 178 taught by Professor Segalman during the Fall '08 term at University of California, Berkeley.
 Fall '08
 SEGALMAN

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